32. Newton's Third Law

1. Defining Newton's Third Law

• The Law: When two objects interact, the forces they exert on each other are equal and opposite.

• Equal: Refers to the magnitude (size) of the two forces.

• Opposite: Refers to the direction in which the forces act.

2. Real-World Examples

• Pushing a Box: If you push a box with a force of 100 N, the box exerts an equal force of 100 N back on you in the opposite direction. This is often called the normal contact force.

• Pushing off a Wall: When you push against a wall, the wall pushes back on you with an equal force. Because the wall is fixed and has immense mass, you are the one who moves backward.

• Jumping: When you jump, you push down on the ground, and the ground pushes back up on you, causing you to move upwards.

3. Relating to Newton's Second Law ($F=ma$ )

While the forces are always equal in size, the effect of those forces (acceleration) depends on the mass of the objects.

Using the rearranged equation $a=\frac{F}{m}:$

• Small Mass: If an object has a small mass, the force will cause a large acceleration, making it move easily.

• Large Mass: If an object has a very large mass, the same force will result in a very small acceleration, making it move much less or not at all.

• Result: This explains why, when a person pushes a small box, the box moves, but when a person pushes a wall, the person moves.

• 4. Summary Table

  Aspect	Description
  Interaction	Occurs between two different objects.
  Magnitude	Always identical for both forces.
  Direction	Always exactly opposite.
  Outcome	Movement depends on the relative masses of the objects ($a=\frac{F}{m}$ )